A train of short laser pulses may be generated with a so-called mode-coupled laser. In a laser medium, it is possible to incite very many self-oscillations with various frequencies with sufficient bandwidth of a laser transition in the resonator of the laser. The self-oscillations are also referred to as modes. By means of suitable mechanisms it is possible to produce a consistent phase relationship between the self-oscillations. This is called mode synchronization or mode coupling. Due to mode coupling, an emission of short light pluses with a time interval τR corresponding to a circulation period of a laser pulse in the resonator of the laser is effected. The direct result of the temporal equidistance of the pulses is that the frequency spectrum of such a laser consists of equidistant individual lines, a so-called frequency comb. Due to this relationship, a method, or a device, respectively, generating such a train of short laser pulses or a modified train of short laser pulses may also be referred to as a method, or device, respectively, for generating a frequency comb. The distance in the frequency space between the individual lines Δf corresponds to an inverse value of the circulation period in the resonator τR. Thus, there applies: Δf=1/τR.
From the article “Route to phase control of ultrashort light pulses” by L. Xu et al., Opt. Lett. 21, 2008 et seq. (1996) it is known that the frequencies fi of the individual lines i are no integer multiples of the difference frequency Δf. Rather, the following relation exists for the frequencies fi of the individual lines i: fi=fCEO+iΔf. Here, fCEO indicates an offset frequency referred to as carrier envelope offset (CEO) frequency in literature. This offset frequency is caused by the fact that the group velocity of the laser pulses deviates from the phase velocity of the individual superposed laser modes, or individual lines, respectively. Typically, the electrical field of the individual laser modes propagates with a slightly higher phase velocity through the electrical media in the resonator of the laser than the envelope of the laser pulse. This results in a phase offset ΔφCEO=2πfCEO τR between the envelope and the individual modes with every circulation in the resonator. With respect to time this offset means that a time offset occurs between the occurrence of a maximum amplitude of the electrical field and the occurrence of the maximum amplitude of the envelope. This time offset is frequently also referred to as carrier envelope offset phase ΔφCEO, although the time offset is correctly given by ΔTCEO=ΔφCEO/2πν0, wherein ν0 is the carrier frequency of the laser pulse.
Since the magnitude of the carrier envelope offset frequency fCEO is severely dependent on environmental factors, e.g. the temperature and the air pressure, but also the pumping performance of the laser medium, etc. so as to list just a few, but not all factors, the carrier envelope offset frequency is moreover not stable with respect to time.
In prior art, various methods have been proposed for determining the carrier envelope offset frequency fCEO. In the publication “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation” by H. R. Telle et al., Appl. Phys. B 69, 327 et seq. (1999), some possible methods are described. So-called f-to-2f interference methods in which part of the laser signal is conducted into an interferometer are most frequently used. In the interferometer a non-linear optical process is utilized to generate the second harmonic of a low-energy laser mode or of a low-energy individual line of the frequency comb, respectively, and to bring it to interference with a high-energy (high-frequency) individual line of the frequency comb of the laser pulse. If fi is the frequency from the low-energy region of the frequency comb fi=i·Δf+fCEO, 2fi=(2iΔf+2fCEO) applies after the frequency doubling. Thus, if this frequency-doubled individual line is brought to interference with an individual line having the double frequency, i.e. f2i=2iΔf+fCEO, then 2fi−f2i=(2iΔf+2fCEO)−(2iΔf+fCEO)=fCEO results for the beat signal. The frequency of the beat signal thus directly indicates the carrier envelope offset frequency.
For some applications it is sufficient to know the carrier envelope offset frequency. For other applications it is, however, desirable and/or necessary to keep the phase offset between the underlying electrical field and the envelope of the laser pulse constant, preferably to minimize it to zero.
This is, for instance, of advantage and/or necessary when generating short pulses with pulse lengths in the range of attoseconds.
DE 199 11 103 A1 discloses a method and a device for generating short laser pulses, as well as the use thereof for synthesizing optical frequencies. In a stabilized laser device in which laser pulses circulating in a resonator arrangement, and that are each composed of spectral components corresponding to a plurality of longitudinal modes of the resonator arrangement are generated every mode is, by a predetermined setting of the linear dispersion of the resonator arrangement, subject to a spectral-specific frequency change. There is described a control for the simultaneous setting of the dispersion and of the resonator length by means of which the group and phase circulation times of the light pulses circulating in the resonator are controlled. The setting of the dispersion may, for instance, be achieved by inserting wedge prisms into the beam path. Alternatively and/or additionally, the resonator may comprise a pivotable end mirror. The measures proposed for changing the dispersion necessarily result in a change of the optical path length and/or in a change of the resonator circulation period τR, i.e. the time interval of the of the light pulses changes. In order to keep this interval and/or the frequency distance of the individual lines Δf constant, a further control is required which controls, for instance, the resonator length. The methods and devices described in DE 199 11 103 A1 each require at least two control circuits influencing each other to keep the carrier envelope offset frequency fCEO and the resonator circulation period τR and/or the repetition frequency frep corresponding to the frequency distance Δf constant. The effort with respect to the apparatus is correspondingly high. Since mechanical movements of optical components are required in the resonator of the laser, the regular bandwidths that are achievable are generally restricted to few kHz. A far quicker control may be achieved pursuant to DE 199 11 103 A1 by a variation of the pumping performance of the laser oscillator by acousto-optical or electro-optical modulators. This, however, influences the peak power of the pulses circulating in the resonator, which in turn manipulates the phase offset ΔφCEO by non-linear optical processes. While acousto-optical modulators are restricted to regular bandwidths of up to approximately 100 kHz, electro-optical systems may reach regular bandwidths in the MHz range. The systems are, however, limited due to the control electronics. Since a free oscillation build-up has to be avoided, the regular amplification is typically limited. This in turn results in that very quick interference components of the ΔφCEO signal (so-called “glitches”) can be compensated insufficiently only.
US 2007/0086713 A1 describes a frequency standard based on a mode-coupled fiber laser. The carrier envelope offset frequency is determined and used, via a phase lock loop circuit, for controlling laser parameters such as, for instance, the pumping power or the temperature of a Bragg grating so as to stabilize the carrier envelope offset frequency itself, i.e. to set it to a constant value.
Irrespective of the exact design, no laser systems are known in prior art in which, by a stabilization of the value of the carrier envelope offset frequency fCEO, other laser parameters such as, for instance, the laser power, the pulse duration, or the pulse repetition rate that is identical with the circulation frequency are not influenced, too.
The technical problem underlying the invention is therefore to provide a method and a device generating a frequency comb in which the carrier envelope offset frequency is stabilized, preferably compensated.